Exact Quasiparticle Properties of a Heavy Polaron in BCS Fermi Superfluids.

We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using the exact functional determinant approach. We describe the Fermi superfluid through the conventional Bardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap on quasiparticle properties revealed by the two spectroscopies. The energy cost for pair breaking prevents Anderson's orthogonality catastrophe that occurs in a noninteracting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity limit. Hence, we rigorously confirm the remarkable features such as dark continuum, molecule-hole continuum, and repulsive polaron. For a magnetic impurity scattering at finite temperature, we predict additional resonances related to the subgap Yu-Shiba-Rusinov bound state, whose positions can be used to measure the superfluid pairing gap. For a nonmagnetic scattering at zero temperature, we surprisingly find undamped repulsive polarons. These exact results might be readily observed in quantum gas experiments with Bose-Fermi mixtures that have a large-mass ratio.

Consistent Theory of Self-Bound Quantum Droplets with Bosonic Pairing.

We revisit the Bogoliubov theory of quantum droplets proposed by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302] for an ultracold Bose-Bose mixture, where the mean-field collapse is stabilized by the Lee-Huang-Yang quantum fluctuations. We show that a loophole in Petrov's theory, i.e., the ignorance of the softening complex Bogoliubov spectrum, can be naturally removed by the introduction of bosonic pairing. The pairing leads to weaker mean-field attractions, and also a stronger Lee-Huang-Yang term in the case of unequal intraspecies interactions. As a result, the equilibrium density for the formation of self-bound droplets significantly decreases in the deep droplet regime, in agreement with a recent observation from diffusion Monte Carlo simulations. Our construction of a consistent Bogoliubov theory paves the way to understand the puzzling low critical number of small quantum droplets observed in the experiment [C. Cabrera et al., Science 359, 301 (2018)SCIEAS0036-807510.1126/science.aao5686].

Few-Body Perspective of a Quantum Anomaly in Two-Dimensional Fermi Gases.

A quantum anomaly manifests itself in the deviation of the breathing mode frequency from the scale invariant value of 2ω in two-dimensional harmonically trapped Fermi gases, where ω is the trapping frequency. Its recent experimental observation with cold atoms reveals an unexpected role played by the effective range of interactions, which requires a quantitative theoretical understanding. Here we provide accurate, benchmark results on a quantum anomaly from a few-body perspective. We consider the breathing mode of a few trapped interacting fermions in two dimensions up to six particles and present the mode frequency as a function of scattering length for a wide range of effective range. We show that the maximum quantum anomaly gradually reduces as the effective range increases while the maximum position shifts towards the weak-coupling limit. We extrapolate our few-body results to the many-body limit and find a good agreement with the experimental measurements. Our results may also be directly applicable to a few-fermion system prepared in microtraps and optical tweezers.

Roton-Induced Bose Polaron in the Presence of Synthetic Spin-Orbit Coupling.

We predict the existence of a roton-induced Bose polaron for an impurity immersed in a three-dimensional Bose-Einstein condensate with Raman-laser-induced spin-orbit coupling, where the condensate is in a finite-momentum plane-wave state with an intriguing roton minimum in its excitation spectrum. This novel polaron is formed by dressing the impurity with roton excitations, instead of phonon excitations as in a conventional (i.e., phonon-induced) Bose polaron, and acquires a significant center-of-mass momentum and highly anisotropic effective mass. We find that the roton-induced polaron evolves from a phonon-induced polaron, as the interaction between impurity and atoms increases across a Feshbach resonance. The evolution is not smooth, and a first-order phase transition from a phonon- to roton-induced polaron is observed at a critical interaction strength.

Cluster Formation in Two-Component Fermi Gases.

Two-component fermions are known to behave like a gas of molecules in the limit of Bose-Einstein condensation of diatomic pairs tightly bound with zero-range interactions. We discover that the formation of cluster states occurs when the effective range of two-body interaction exceeds roughly 0.46 times the scattering length, regardless of the details of the short-range interaction. Using an explicitly correlated Gaussian basis set expansion approach, we calculate the binding energy of cluster states in trapped few-body systems and show the difference of structural properties between cluster states and gaslike states. We identify the condition for cluster formation and discuss the potential observation of cluster states in experiments.

Reduced Quantum Anomaly in a Quasi-Two-Dimensional Fermi Superfluid: Significance of the Confinement-Induced Effective Range of Interactions.

A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale-invariant value ω_{B}=2ω_{⊥}, where ω_{⊥} is the trapping frequency. The predicted maximum quantum anomaly (∼10%) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single s-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions.

Realizing Fulde-Ferrell Superfluids via a Dark-State Control of Feshbach Resonances.

We propose that the long-sought Fulde-Ferrell superfluidity with nonzero momentum pairing can be realized in ultracold two-component Fermi gases of ^{40}K or ^{6}Li atoms by optically tuning their magnetic Feshbach resonances via the creation of a closed-channel dark state with a Doppler-shifted Stark effect. In this scheme, two counterpropagating optical fields are applied to couple two molecular states in the closed channel to an excited molecular state, leading to a significant violation of Galilean invariance in the dark-state regime and hence to the possibility of Fulde-Ferrell superfluidity. We develop a field theoretical formulation for both two-body and many-body problems and predict that the Fulde-Ferrell state has remarkable properties, such as anisotropic single-particle dispersion relation, suppressed superfluid density at zero temperature, anisotropic sound velocity, and rotonic collective mode. The latter two features can be experimentally probed using Bragg spectroscopy, providing a smoking-gun proof of Fulde-Ferrell superfluidity.

Traveling Majorana Solitons in a Low-Dimensional Spin-Orbit-Coupled Fermi Superfluid.

We investigate traveling solitons of a one- or two-dimensional spin-orbit-coupled Fermi superfluid in both topologically trivial and nontrivial regimes by solving the static and time-dependent Bogoliubov-de Gennes equations. We find a critical velocity v_{h} for traveling solitons that is much smaller than the value predicted using the Landau criterion due to spin-orbit coupling. Above v_{h}, our time-dependent simulations in harmonic traps indicate that traveling solitons decay by radiating sound waves. In the topological phase, we predict the existence of peculiar Majorana solitons, which host two Majorana fermions and feature a phase jump of π across the soliton, irrespective of the velocity of travel. These unusual properties of Majorana solitons may open an alternative way to manipulate Majorana fermions for fault-tolerant topological quantum computations.

Gapless topological Fulde-Ferrell superfluidity in spin-orbit coupled Fermi gases.

Topological superfluids usually refer to a superfluid state which is gapped in the bulk but metallic at the boundary. Here we report that a gapless, topologically nontrivial superfluid with an inhomogeneous Fulde-Ferrell pairing order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas, in the presence of both in-plane and out-of-plane Zeeman fields. The Fulde-Ferrell pairing-induced by the spin-orbit coupling and in-plane Zeeman field-is responsible for this gapless feature. This exotic superfluid has a significant Berezinskii-Kosterlitz-Thouless transition temperature and has robust Majorana edge modes against disorder owing to its topological nature.

Universal impurity-induced bound state in topological superfluids.

We predict a universal midgap bound state in topological superfluids, induced by either nonmagnetic or magnetic impurities in the strong scattering limit. This universal state is similar to the lowest-energy Caroli-de Gennes-Martricon bound state in a vortex core, but is bound to localized impurities. We argue that the observation of such a universal bound state can be a clear signature for identifying topological superfluids. We theoretically examine our argument for a spin-orbit coupled ultracold atomic Fermi gas trapped in a two-dimensional harmonic potential by performing extensive self-consistent calculations within the mean-field Bogoliubov-de Gennes theory. A realistic scenario for observing a universal bound state in ultracold 40K atoms is proposed.

Spin-orbit coupled weakly interacting Bose-Einstein condensates in harmonic traps.

We investigate theoretically the phase diagram of a spin-orbit coupled Bose gas in two-dimensional harmonic traps. We show that at strong spin-orbit coupling the single-particle spectrum decomposes into different manifolds separated by ℏω{⊥}, where ω{⊥} is the trapping frequency. For a weakly interacting gas, quantum states with Skyrmion lattice patterns emerge spontaneously and preserve either parity symmetry or combined parity-time-reversal symmetry. These phases can be readily observed in a spin-orbit coupled gas of ^{87}Rb atoms in a highly oblate trap.

Probing anisotropic superfluidity in atomic Fermi gases with Rashba spin-orbit coupling.

Motivated by the prospect of realizing a Fermi gas with a synthetic non-Abelian gauge field, we investigate theoretically a strongly interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the twofold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet components emerge, leading to an anisotropic superfluid. We calculate the relevant physical quantities, such as the momentum distribution, the single-particle spectral function, and the spin structure factor, that characterize the system.

Pseudogap pairing in ultracold Fermi atoms.

The Bose-Einstein condensate to Bardeen-Cooper-Schrieffer crossover in ultracold Fermi gases creates an ideal environment to enrich our knowledge of many-body systems. It is relevant to a wide range of fields from condensed matter to astrophysics. The nature of pairing in strongly interacting Fermi gases can be readily studied. This aids our understanding of related problems in high-Tc superconductors, whose mechanism is still under debate due to the large interaction parameter. Here, we calculate the dynamical properties of a normal, trapped strongly correlated Fermi gas, by developing a quantum cluster expansion. Our calculations for the single-particle spectral function agree with recent rf spectroscopy measurements, and clearly demonstrate pseudogap pairing in the strongly interacting regime.

Virial expansion for a strongly correlated Fermi gas.

Using a high temperature virial expansion, we present a controllable study of the thermodynamics of strongly correlated Fermi gases near the BEC-BCS crossover region. We propose a practical way to determine the expansion coefficients for both harmonically trapped and homogeneous cases, and calculate the third order coefficient b{3}(T) at finite temperatures T. At resonance, a T-independent coefficient b{3,infinity};{hom} approximately -0.290 952 95 is determined in free space. These results are compared with a recent thermodynamic measurement of 6Li atoms, at temperatures below the degeneracy temperature, and with Monte Carlo simulations.

Visualization of vortex bound states in polarized fermi gases at unitarity.

We theoretically analyze a single vortex in a spin polarized 3D trapped atomic Fermi gas near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied by the majority spin component. As a result, the local density difference at the core center suddenly rises at low temperatures. This provides a way to visualize the lowest bound state using phase-contrast imaging. As the polarization increases, the core expands gradually and the energy of the lowest bound state decreases.

Phase diagram of a strongly interacting polarized Fermi gas in one dimension.

Based on the integrable Gaudin model and local density approximation, we discuss the ground state of a one-dimensional trapped Fermi gas with imbalanced spin population, for an arbitrary attractive interaction. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density compressional mode. We identify the polarized superfluid as having an Fulde-Ferrell-Larkin-Ovchinnikov structure, and predict the resulting mode frequency as a function of the spin polarization.

Signature of Mott-insulator transition with ultracold fermions in a one-dimensional optical lattice.

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Collective modes and ballistic expansion of a fermi gas in the BCS-BEC crossover.

We evaluate the frequencies of collective modes and the anisotropic expansion rate of a harmonically trapped Fermi superfluid at varying coupling strengths across a Feshbach resonance driving a BCS-BEC crossover. The equations of motion for the superfluid are obtained from a microscopic mean-field expression for the compressibility and are solved within a scaling ansatz. Our results confirm nonmonotonic behavior in the crossover region and are in quantitative agreement with current measurements of the transverse breathing mode by Kinast et al. [Phys. Rev. Lett. 92, 150402 (2004)]] and of the axial breathing mode by Bartenstein et al. [Phys. Rev. Lett. 92, 203201 (2004)]].